In the second section, we will begin by considering several classical solutions of \(\frac{1}{2}\) -BPS M5 probe branes in \(AdS_7 \times S^4\)  background expressed in the global coordinates. The equations that define the worldvolume of these probe M5s are analogous to the ones used for probe D3 brane solutions [1]}, [2]} which were used to study the BPS monodromy defects in \(\mathcal {N}=4\)  SYM theory holographically. These are noncompact brane solutions with world-volume toplogy of \(AdS_5 \times S^1\)  ending on the boundary in \(\mathbb {R} \times S^3\)  submanifold. They are one of the new findings that appear in this manuscript. The intersection of these M5 brane probes with the boundary should essentially be the half-BPS codimension-2 defects in the \(6d\)  \((0,2)\)  theory on \(\mathbb {R} \times S^5\) . We perform a \(\kappa \) -symmetry analysis to find the projections on the bulk Killing spinor for the various \(\frac{1}{2}\) -BPS probes. In section 3, we use the common supersymmetry of all the half-BPS probe solutions to derive the general BPS equations whose solutions preserve the least amount of supersymmetry from the ambient 11 dimensional geometry. A common single supersymmetry also comes from those half-BPS solutions which have compact world-volumes and are more commonly referred as the dual-giant gravitons in the literature [3]}, [4]}. The worldvolume of the general probe branes are described by zeros of the holomorphic functions that satisfy a scaling condition. The general expression that we derive here give the worldvolumes of the least supersymmetric probe M5 branes in the \(AdS_7 \times S^4\)  geometry which include the dual-giant graviton configurations as well as the holographic dual of codimension-2 defects in the boundary 6d gauge theory. In section 4, we look at those M5 brane solutions that wrap a circle in the \(S^4\)  part of the geometry, they are in general \(\frac{1}{8}\) -BPS configurations. We do the analysis near the boundary of \(AdS_7\) , and we show how the zero locus of the holomorphic function should coincide with the location of codimension-2 defect in the \(\frac{1}{8}\) -BPS sector of the \(6d\)  \((0,2)\)  theory. Moreover, we also propose that the \(\frac{1}{8}\) -BPS defects have a general characterisation which describes them as the intersection of the zeros of a holomorphic function \(F(z_1, z_2, z_3) = 0\)  with the 5-sphere defined by \(|z_1|^2 + |z_2|^2 + |z_3|^2 = 1\) . This analysis of the general \(\frac{1}{8}\) -BPS probe M5 brane near the boundary of \(AdS\)  also suggests us the kind of singular behavior the bosonic fields in the 6d theory may acquire near the location of the defect.
